Yes but those chips have only one output and several inputs exactly the opposite of what is needed.

A standard video signal is 1V park to peak. That amplifier circuit is a very poor circuit as you can tell from the trace. All those sync pulses should be flat at the same zero volts level. This is because there is no black level clamping in the circuit and the circuit is DC coupled.You need an AC coupled input and some clamping. Then you need four of them to drive a seprate output each. You can't chain video signals.